"it didn't look like I could provide multiple keys"

Ask and you shall receive. Oh wait, you didn't ask, well no matter...

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11111952
use warnings;
use List::Util qw( none any );
use Data::Dump qw( dd );

sub subtree
  {
  my ($key, $tree) = @_;
  if( ref $tree eq 'ARRAY' )
    {
    my @items = map [ subtree( $key, $_ ) ], @$tree;
    return +(none { $_->[0] } @items ) ? ( 0, []) :
      ( 1, [ map { $_->[0] ? $_->[1] : undef } @items ] );
    }
  elsif( ref $tree eq 'HASH' )
    {
    my @wanted;
    for my $k ( sort keys %$tree )
      {
      if( matchkey( $key, $k ) ) { push @wanted, [ 1, $k => $tree->{$k
+} ] }
      else
        {
        my ( $w, $t ) = subtree( $key, $tree->{$k} );
        $w and push @wanted, [ $w, $k => $t ];
        }
      }
    return @wanted > 0, +{ map { @{ $_ }[1, 2] } @wanted };
    }
  else { return 0, $tree }
  }

sub matchkey
  {
  my ($key, $here) = @_;
  any { $_ eq $here } ref $key ? @$key : $key;
  }

sub pathforkey
  {
  my ($key, $tree, $sofar) = @_;
  if( ref $tree eq 'HASH' )
    {
    return map {  
      matchkey( $key, $_ ) ? $sofar . "{$_}" : (),
      pathforkey( $key, $tree->{$_}, $sofar . "{$_}" )
      } sort keys %$tree;
    }
  elsif( ref $tree eq 'ARRAY' )
    {
    return map { pathforkey( $key, $tree->[$_], $sofar . "[$_]" )
      } 0 .. $#$tree;
    }
  else { return () }
  }

my $tree = gettree();
dd 'original tree', $tree;
print "\n";
my ($want, $subtree) = subtree( [ 'field', '_mcid' ], $tree );
dd "the subtree for 'field' ", $subtree;
print "\nall paths to key 'field' :\n";
print "$_\n" for pathforkey( ['field', '_mcid'], $tree, '' );

sub gettree # slightly reduced...
  {
  my $tree = { 'cookies' => { '_AVESTA_ENVIRONMENT' => 'prod',
    '_mcid' => '1.340667ccb3eb6552450356561ab6bd92.' },
      'error' => '400 Bad Request',
      'content' => { 'detail' =>
      'The resource specific details, \'errors\' array.',
      'errors' => [ 'not this', { 'message' => 'This value of type obj
+ect.',
        'field' => 'merge_fields' } ],
      'status' => 400,
      'title' => 'Invalid Resource',
      'type' => 'http://developer.mailchimp.',
      'instance' => '59edf1fc-ed93-4a40-ba23-1f0af24a6eb3' },
      'code' => '400' };
  }
[download]

Outputs:

(
  "original tree",
  {
    code    => 400,
    content => {
                 detail   => "The resource specific details, 'errors' 
+array.",
                 errors   => [
                               "not this",
                               { field => "merge_fields", message => "
+This value of type object." },
                             ],
                 instance => "59edf1fc-ed93-4a40-ba23-1f0af24a6eb3",
                 status   => 400,
                 title    => "Invalid Resource",
                 type     => "http://developer.mailchimp.",
               },
    cookies => {
                 _AVESTA_ENVIRONMENT => "prod",
                 _mcid => "1.340667ccb3eb6552450356561ab6bd92.",
               },
    error   => "400 Bad Request",
  },
)

(
  "the subtree for 'field' ",
  {
    content => { errors => [undef, { field => "merge_fields" }] },
    cookies => { _mcid => "1.340667ccb3eb6552450356561ab6bd92." },
  },
)

all paths to key :
{content}{errors}[1]{field}
{cookies}{_mcid}
[download]